In the role, Jones will take responsibility for electrical, stationery, home, toys, entertainment, papershop and global sourcing.
He joined Sainsbury's in February 2003 and launched the retailer's clothing range Tu, which celebrated its second anniversary in September.
Last month, Sainsbury's said the label was approaching sales of £250m on an annualised basis.
Prior to Sainsbury's he worked at Marks and Spencer for 17 years. "Richard has done a fantastic job launching the Sainsbury's clothing offer and Tu as the UK's fastest growing clothing brand," said Mike Coupe, trading director for Sainsbury's.
"Richard brings a wealth of experience in a number of roles that will benefit Sainsbury's future plans."
Jones will be replaced in the new year, a spokeswoman for Sainsbury's said.